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Simplifying (x + 3)(x + -5) = x * x + 7 Reorder the terms: (3 + x)(x + -5) = x * x + 7 Reorder the terms: (3 + x)(-5 + x) = x * x + 7 Multiply (3 + x) * (-5 + x) (3(-5 + x) + x(-5 + x)) = x * x + 7 ((-5 * 3 + x * 3) + x(-5 + x)) = x * x + 7 ((-15 + 3x) + x(-5 + x)) = x * x + 7 (-15 + 3x + (-5 * x + x * x)) = x * x + 7 (-15 + 3x + (-5x + x2)) = x * x + 7 Combine like terms: 3x + -5x = -2x (-15 + -2x + x2) = x * x + 7 Multiply x * x -15 + -2x + x2 = x2 + 7 Reorder the terms: -15 + -2x + x2 = 7 + x2 Add '-1x2' to each side of the equation. -15 + -2x + x2 + -1x2 = 7 + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -15 + -2x + 0 = 7 + x2 + -1x2 -15 + -2x = 7 + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -15 + -2x = 7 + 0 -15 + -2x = 7 Solving -15 + -2x = 7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -2x = 7 + 15 Combine like terms: -15 + 15 = 0 0 + -2x = 7 + 15 -2x = 7 + 15 Combine like terms: 7 + 15 = 22 -2x = 22 Divide each side by '-2'. x = -11 Simplifying x = -11
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